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arXiv · 2604.15198

Integrable Deformations and Stability of the Ricci Flow

Maxwell Stolarski·Alex Waldron
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Abstract

We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the equivalence between integrability and an "almost-orthogonality" property of the Ricci-DeTurck tensor, allowing us to analyze the latter directly. We obtain our main results in weighted Holder spaces and then show how to recover the $L^p$-stability theorems of Deruelle-Kroncke and Kroncke-Petersen.

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Maxwell Stolarski, Alex Waldron. 2026-04-16. Integrable Deformations and Stability of the Ricci Flow. https://arxiv.org/abs/2604.15198

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